A spinner with 10 equally sized slices is shown below. (3 slices are blue, 2 are yellow, and 5 are rec the probability that the dial stops on a blue or yellow slice? Write your answer as a fraction or a whole number.​

The money he will have in this account if he keeps it for 5 years is $333, if the interest rate is compounded semiannually.

Compound interest is the term used to describe interest on savings that is calculated using both the initial principal and interest that has accrued over time. You can earn interest on interest, which is known as compound interest. Mathematically, if you have $100 and it earns 5% interest annually, you will have $105 at the end of the first year. You will have $110.25 by the conclusion of the second year.

Given,

P=$300

Time t=5 years

Interest rate=2.1%

Hence, the amount will have in his account is:

=\(P(1+(10/2000)^{2t}\)

Here, the interest is compounded semiannually.

=\(300(1+(2.1/200))^{10}\)

=$333

Therefore, the money he will have in this account if he keeps it for 5 years is $333, if the interest rate is compounded semiannually.

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Answer:

...

Step-by-step explanation:

Answer:

The cost of sending the telegram is $6.

Step-by-step explanation:

Since 3 St. Post Office charges for an ordinary telegram are $ 4 for the first 10 words and 40 cents for each extra word, to calculate the cost of sending this telegram: MR KAMAU ARRIVING AT 0630 EAST AFRICAN TIME ON BOARD KQ 46 INFORM THE WIFE must perform the following calculation:

The telegram has 15 words.

4 + ((15 - 10) x 0.40) = X

4 + (5 x 0.40) = X

4 + 2 = X

6 = X

Therefore, the cost of sending the telegram is $ 6.

The domain of the function represented in the graph will be 20 ≤ x ≤ 60, or x is from 20 to 60. Then the correct option is D.

A line segment in mathematics has two different points on it that define its boundaries.

A line segment is sometimes referred to as a section of a path that joins two places.

Six-year-old students at an elementary school were given a 20-yard head start in a race. The graph shows how far the average student ran in 30 seconds.

A line graph with Distance, in yards, on the x-axis and Age of the Runner on the y-axis. The x-axis has a scale from 0 to 80 in increments of 10. The y-axis has a scale of 0 to 8 in increments of 2. A straight line connecting 20, 6, and 60, 6 is drawn.

The domain of the function represented in the graph will be 20 ≤ x ≤ 60, or x is from 20 to 60. Then the correct option is D.

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Answer:

the correct option is D

Step-by-step explanation:

Answer:

x

Step-by-step explanation:

bc the coefficient of x is 1 and that's invisible so it's x

Answer:

- September

Step-by-step explanation:

The temperature in Beijing, in m months after January, is given by the following equation:

\(T(m) = 27\cos{((\frac{\pi}{6})(m-6))} + 45\)

In which m is the number of months after January.

During which month in the year would the temperature reach 55°F?

We have to find m for which: T(m) = 55. So

\(T(m) = 27\cos{((\frac{\pi}{6})(m-6))} + 45\)

\(55 = 27\cos{((\frac{\pi}{6})(m-6))} + 45\)

\(27\cos{((\frac{\pi}{6})(m-6))} = 10\)

\(\cos{((\frac{\pi}{6})(m-6))} = \frac{10}{27}\)

Now, we apply the inverse cosine, on both sides of the equation, to find the value of m.

\(\cos^{-1}{\cos{(\frac{\pi}{6})(m-6)}} = \cos^{-1}{\frac{10}{27}}\)

Now, with the help of a calculator, in radians:

\(\frac{\pi}{6}(m-6) = 1.19\)

\(\pi m - 6\pi = 6*1.19\)

\(\pi m = 6*1.19 + 6 \pi\)

\(m = \frac{6*1.19 + 6 \pi}{\pi}\)

\(m = 8.27\)

8.27 months after January, since 8.27 + 1 = 9.28, it happens during the month of September.

Answer: September

Step-by-step explanation:

Edge

Answer:

The answer is "2.4049"

Step-by-step explanation:

Calculating the test of Hypothesis: \(H_{0}: 23\% \ \text{off all adults which reconize the compony's logo}\\\\H_{1}: \text{more than 23\% of adult recornise the compony's logo}\\\\\)

that is

\(H_{0}: p=0.23\ against \ H_{1}:p>0.01\\\\Z=\frac{P-p}{\sqrt{\frac{p(1-p)}{n}}}\sim N(0,1)\\\\\)

Given:

\(p= 0.23\\\\ \therefore \\\\1-p=0.77\\\\n=1200\\\\ P=\frac{311}{1200}=0.2591\\\\\therefore\\\\Z= \frac{0.2591-0.23}{\sqrt{((0.23)\times \frac{(1-0.23))}{1200}}}=2.4049\)

Z=2.576 tabled value. Because Z is 2.4049, that's less than Z stated, there is no indication that a null hypothesis is rejectable, which means that 23% of all adults record the logo of the Company.

Answer:

  B.  Incorrectly applied the distributive property

Step-by-step explanation:

You want to find Maria's error in her solution of -2(3x -5) = 40.

The solution can proceed as follows:

  -2(3x -5) = 40 . . . . . . . . given

  -6x +10 = 40 . . . . . . . . . use the distributive property

  -6x = 30 . . . . . . . . . . subtract 10

  x = -5 . . . . . . . . . . divide by -6

Comparing this solution to Maria's, we find that Maria incorrectly applied the distributive property. (She multiplied (-2)(-5) and got -10 instead of +10.)

Step-by-step explanation:

The transformation y = sin(2x) affects the graph of y = sin(x) by compressing it horizontally.

The function y = sin(2x) has a coefficient of 2 in front of the x variable. This means that for every x value in the original function, the transformed function will have half the x value.

To see the effect of this transformation, let's compare the graphs of y = sin(x) and y = sin(2x) by plotting some points:

For y = sin(x):

x = 0, y = 0

x = π/2, y = 1

x = π, y = 0

x = 3π/2, y = -1

x = 2π, y = 0

For y = sin(2x):

x = 0, y = 0

x = π/2, y = 0

x = π, y = 0

x = 3π/2, y = 0

x = 2π, y = 0

As you can see, the y-values of the transformed function remain the same as the original function at every x-value, while the x-values of the transformed function are compressed by a factor of 2. This means that the graph of y = sin(2x) appears narrower or more "squeezed" horizontally compared to y = sin(x).

Therefore, the correct statement is: It is compressed horizontally.

Answer:

16 rungs

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

She climbed +2

Move down -2 plus an additional +2

Then climbed +8 and the remaining +2

2 - 2 + 2 + 8 + 2 = 12

I hope this helps!

Part 1

\(a=\sqrt{12^2 + 21^2 -2(12)(21) \cos 35^{\circ}} \approx \boxed{13}\)

Part 2

\(\frac{\sin B}{b}=\frac{\sin A}{a}\\\\\sin B=\frac{b\sin A}{a}\\\\\sin B=\frac{12 \sin 35^{\circ}}{\sqrt{12^2 +21^2 -2(12)(21) \cos 35^{\circ}}}\\\\B=\sin^{-1} \left(\frac{12\sin 35^{\circ}}{\sqrt{12^2 +21^2 -2(12)(21) \cos 35^{\circ}}} \right)\\\\B \approx \boxed{32^{\circ}}\)

Part 3

\(\angle C=180^{\circ}-\angle A -\angle B=\boxed{113^{\circ}}\)

Answer:

x = -9 + 11y

Step-by-step explanation:

Simplifying

2x + -22y = -18

Solving

2x + -22y = -18

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '22y' to each side of the equation.

2x + -22y + 22y = -18 + 22y

Combine like terms: -22y + 22y = 0

2x + 0 = -18 + 22y

2x = -18 + 22y

Divide each side by '2'.

x = -9 + 11y

Simplifying

x = -9 + 11y

Hope this helps!!

Answer:

1100                                                                 brainliest please

Step-by-step explanation:

1000×2×0.05=100

1000+100=110

(a) Solving initial value problem, P(t) = (1/k) [(kPo + M)e^(kt) - M]

(b)To keep P(t) constant and equal to Po, k must be negative and M must be positive.

(a) To solve the initial value problem:

dP/dt = kP + M, P(0) = Po

We can rewrite the differential equation as:

dP/(kP + M) = dt

Integrating both sides, we get:

(1/k) ln|kP + M| = t + C

where C is a constant of integration. Solving for P, we get:

P(t) = (1/k) (e^(k(t+C)) - M/k)

To find the value of C, we use the initial condition P(0) = Po:

Po = (1/k) (e^(kC) - M/k)

Solving for C, we get:

C = (1/k) ln(kPo + M) - (1/k) ln|kPo|

Substituting this back into the expression for P(t), we get:

P(t) = (1/k) [(kPo + M)e^(kt) - M]

(b) To determine the conditions under which P(t) remains constant and equal to Po, we set P(t) = Po and solve for k and M:

Po = (1/k) [(kPo + M)e^(kt) - M]

Simplifying and rearranging, we get:

(k - 1)e^(kt) = M/Po

If k = 1, then we get 0 = M/Po, which is impossible unless M = 0 (i.e., there is no migration). Therefore, we assume k ≠ 1.

Taking the natural logarithm of both sides, we get:

kt + ln(k - 1) = ln(M/Po)

Solving for k, we get:

k = [ln(M/Po) - ln(k - 1)]/t

To keep P(t) constant and equal to Po, k must be negative (i.e., P(t) is decreasing) and M must be positive (i.e., there is net migration into the population). Physically, this makes sense because if the migration rate is positive, then more individuals are entering the population than leaving, which will tend to increase the population size. Conversely, if the growth rate k is negative, then the population is decreasing in the absence of migration, so the positive migration rate can counteract this decrease and maintain a constant population size.

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Answer:

\(\frac{-1.1x^{25} }{-1.1x^{11} }\)     \(\frac{mx^{67} }{mx^{37} }\)

Step-by-step explanation:

Sine (-1.1) is the same as (-1.1) you just put them together and if the numbers are by each other you just add up the exponents. But if the question says this \(\frac{-1.1x^{2} }{-1.1x^{3} }\) than you subtract the exponents.

·\((-1.1)x^{13}X (-1.1)x^{12} = add\\\frac{-1.1x^{2} }{-1.1x^{2} } = subtract\)

Hope this helps. Have a blessed day :)

Answer:

depth 5 8.3 ft, length 5 24.9 ft, width 5 16.8 ft

Question A is the survey that you expect to have fair results regarding attitudes about carnivals

This survey question is the most neutral and fair among the options provided. It doesn't include any leading or biased language that may influence the respondent's answer.

Option B uses the adjective "exciting," which could lead people to think positively about carnivals.

Option C brings in the unrelated factor of "traveling across town," which could negatively influence the response based on travel preference rather than attitude towards carnivals. Option D uses negative descriptors "noisy" and "overpriced," which could lead people to think negatively about carnivals.

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The statement which best describes the data given is C) The data can be modeled by a quadratic function.

Given a data,

The numbers of customers that visited a store each hour for several hours after the store opened at 8 am are shown in the table.

It is clear that the number of customers increases to 18 for the first 4 hours and then decreases to 0 after 9 hours.

So this data cannot be modeled by a linear function or an exponential function.

Also since the number of customers arriving is not constant, this cannot be expressed as constant function.

So it is quadratic function.

Hence the correct option is c.

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Answer:

n=1/3

Step-by-step explanation:

Answer:

There’s no error

Step-by-step explanation:

The three (3) statements which are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   ....equation 1.

Where:

h and k represents the coordinates at the center of a circle.

r represents the radius of a circle.

From the information provided above, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

Comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius (r) = 3

Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).

(x – 0)² + (y - 0)² = 3²

x² + y² = 9.

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Answer:

P = 0.309

Step-by-step explanation:

Answer:

-$7.20

Step-by-step explanation:

28.75 - 35.95 = 7.20

By Pythagorean theorem, the maze is solved in the following way: x = 6√5 → x = 2√5 → x = 13√5 → x = 2√41 → x = 18√2 → x = 4√6 → x = 4√41 → x = 8√3 → x = 8√5

In this problem we need to complete a maze by means of Pythagorean theorem, whose definition is now introduced:

r² = x² + y²

Where:

Now we proceed to solve the maze:

Step 1:

x = √(12² + 6²)

x = 6√5

Step 2:

x = √(6² - 4²)

x = 2√5

Step 3

x = √(22² + 19²)

x = 13√5

Step 4

x = √(8² + 10²)

x = 2√41

Step 5

x = √(27² - 9²)

x = 18√2

Step 6

x = √(14² - 10²)

x = 4√6

Step 7

x = √(16² + 20²)

x = 4√41

Step 8

x = √(16² - 8²)

x = 8√3

Step 9

x = √(24²- 16²)

x = 8√5

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HbcnAnswer:bfn

Step-by-step explanation:vngc

Answer:

12.5%

Step-by-step explanation:

26 out of 208 is equal to 'x' out of 100

208x=2600

x=12.5

Answer:

firs find the least common multiple (LCM) of the denominators

Step-by-step explanation:

2/5+7/10

Multiples of 5 = {5,10,15,20,25,30,35...}

Multiples of 10 = {10,20,30,40,50...}

Common multiples = {10,20,30,...}

Least Common Multiples = {10}

2/5+7/10

= 2(2) + 7(1)

= 11/LCM

But the LCM = 10

11/10

In this problem we have that

mso

the formula to calculate the interior angle is equal to

msubstitute the given values

m

therefore

Answer:

The population of the town will be 1771.44663 in 6 years.

Here is the calculation:

1400 * (1.04)^6 = 1771.44663

The formula for calculating the population of a town after a certain number of years is:

Population after n years = Initial population * (1 + growth rate)^n

In this case, the initial population is 1400, the growth rate is 4%, and the number of years is 6.

Plugging these values into the formula, we get:

Population after 6 years = 1400 * (1 + 0.04)^6 = 1771.44663

Step-by-step explanation:

Answer:

12,070,000mm'

Step-by-step explanation:

Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

Answer:

c. 0.10

Step-by-step explanation:

Hello!

To accept a batch of components, the proportion of defective components is at most 0.10.

X: Number of defective components in a sample of 10.

This variable has a binomial distribution with parameters n=10 and p= 0.10 (for this binomial experiment, the "success" is finding a defective component)

The distributor will accept the batch if at most two components are defective, symbolically:

P(X≤2)

Using the tables for the binomial distribution you can find the accumulated probability for a sample of n=10 with probability of success of p= 0.10 and number of successes x= 2

P(X≤2)= 0.9298

I hope this helps!